Popcorn Time did this and it worked great. Starting a torrent wasn't instant, but once a buffer was built up, it streamed just fine.

Popcorn Time got taken down pretty hard because they became too popular too fast.

A commercial solution could have a seed server optimized for streaming the initial segments of video files to kickstart the stream, and let basic torrents deal with the rest of the stream.

Popcorn Time still works and used by everyone who cares. It's just not as hyped anymore.